How to Berkeley: Linear System Theory Prelim

Having just spent the last 3.5 weeks doing not much other than prepare for prelims, I thought I would summarize my experience and give some insights.

For starters, prelims are short for preliminary examination, an oral exam that is one of many requirements in your PhD journey at Berkeley (in EECS). The pass rate for this exam is on the order of 70-85%, though you are allowed to take it twice (or thrice, with a petition), and the overall pass rate is about 95%. [Disclaimer: these numbers are 2nd hand. They are approximate.] The exam takes place over 1 hour, with 3 professors. Each professor gives you 20 minutes (though it has been 16 minutes the last couple years) to solve some problems on the board. The topic of my prelim exam was linear system theory, meaning linear algebra and linear control theory. The highest order bit for success on this exam is taking EE221A (or already knowing the material).

Why take the prelim? What is it useful for?
Here are some perspectives I found interesting from some of the older (and wiser) students.
– “You’ll never feel as smart as you did when you took your prelim. That is the culmination of your expertise.” – Roy Dong
– “There is almost no correlation between how much of the question you get through and whether or not you pass. The thing to keep in mind for how they determine your score is ‘would you benefit from taking the prelim again?'”
In some sense, the prelim is as much testing your mastery of the content as it is testing how much you can think on the spot (and take hints/guidance from the committee), explain concepts, and present on the board.

Focused learning
Never in my life have I been so free for so long to focus on one thing. There have always been extra curriculars, homework, classes, social obligations, miscellaneous other responsibilities that chip away at life, hour by hour. 4 weeks ago, I wondered: “how long can you focus?” And it is amazing how much you can do and learn when you put your heart/mind into something. So, what can I accomplish if I put the same amount of focus into something else? I don’t know that a pure focus approach is suitable always, but it really is a key part of grad school and doing research.

Being healthy
This is actually just a continuation of things I’m learning after college. 🙂 Oddly, there was never much incentive in my life to be healthy. Over the last month, I was healthier than I ever was. I took the time to eat enough, sleep enough, relax enough, and even exercise! I told most people ‘sorry, I’m MIA this month, poke me in September?’ There was nothing but prelims and me time (okay, and also a journal paper deadline 3 days after the prelim). Pushing everything else aside, reminded that I can be free (aside from prelims).

Now, without prelims, can I still be free?

How do you prepare for the prelim?
I stumbled around a bit at the beginning, not knowing quite where to start, how to split my time between the paper and studying, and being irked by the typeset of the Callier and Desoer book. Eventually (by the last week), I fell into a nice routine of:

  1. Do old prelim problems.
  2. Note down confusions. Note down topics to learn/review.
  3. Discuss confusions with study group.
  4. Read/review topics.
  5. Repeat.

I recommend getting into that routine sooner. I also spent the last 2 days before the exam going through the lecture notes from EE221A, to pick up anything I might have missed in ad hoc studying, which I also recommend. Preparation will vary from person to person, but the general advice for preparation seems to be:

  • Get a good study group and study with them. Early and often.
  • Ask older students for help, e.g. through mock exams.
  • Relax the day before the exam. (And have great friends who convince you to do so. 🙂 )

The actual prelim
You study for a few weeks, discussing question after question, reviewing topic after topic. It all seems to be building up to something grand. You calm yourself the couple hours before the exam with some hot tea and a good book, unsure how you’ll perform when it matters. But then you go in to the examination room, a professor hands you a question and tells you you have 16 minutes, and you get started just like that. You cite theorems, sketch some proofs, and describe your intuition. You remain brief because there’s a lot to get through. You work out small examples when you are unsure of the full approach. Along the way, the professors attempt to hint you along. And you chug chug chug along. 48 minutes later, you thank the committee and leave the room. That’s it. The prelim exam itself is fully expected, almost routine. The bulk of the gains (learning, making friends, etc.) happen beforehand. So, don’t have too high expectations for the prelim exam itself. 🙂

Additional study references
– Modern Control System Engineering, in particular Chapters 3,5,10 [link] — great for perspective on modern vs classical control, control tools
– Linear Algebra Done Right — self-explanatory

Special thanks to Eric Kim for feedback on this post. Also thanks to all the friends who helped us prepare!

Update: average rating of the overall prelim experience this year is 7.8/10. Caution: statistics is dangerous, sample may be biased.

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